A blimp is ascending at the rate of 7.50 m / s at a height of 80.0 m above the ground when a p

step 1 A blimp is ascending or rising in a vertical direction at 7 .50 meters per second, and at a heig

A blimp is ascending at the rate of 7.50 m / s at a height...

A blimp is ascending at the rate of $7.50 \mathrm{~m} / \mathrm{s}$ at a height of $80.0 \mathrm{~m}$ above the ground when a package is thrown from its cockpit horizontally with a speed of $4.70 \mathrm{~m} / \mathrm{s}$. a) How long does it take for the package to reach the ground? b) With what velocity (magnitude and direction) does it hit the ground?

A blimp is ascending at the rate of $7.50 \mathrm{~m} / \mathrm{s}$ at a height of $80.0 \mathrm{~m}$ above the ground when a package is thrown from its cockpit horizontally with a speed of $4.70 \mathrm{~m} / \mathrm{s}$.
a) How long does it take for the package to reach the ground?
b) With what velocity (magnitude and direction) does it hit the ground?

Key Concepts

Projectile Motion

Projectile motion involves the movement of an object that is launched into the air and is subject only to the acceleration due to gravity. In such motion, the horizontal and vertical components of the object’s velocity are treated independently, allowing calculations for time of flight, range, and final velocity by solving the kinematic equations separately in each direction.

Decomposition of Motion

Decomposition of motion refers to breaking down a vector into its horizontal and vertical components. This concept is essential in projectile problems because it permits the independent analysis of the motion, recognizing that while the horizontal component of velocity remains constant (if air resistance is neglected), the vertical component is affected by gravitational acceleration.

Kinematic Equations

Kinematic equations are used to describe the motion of an object under constant acceleration. They are fundamental for solving problems in projectile motion, including calculating displacement, initial velocity contributions, time of flight, and final velocity magnitude when acceleration is known.

Quadratic Equations in Kinematics

When solving for time of flight in projectile motion problems, the vertical displacement equation often takes the form of a quadratic equation. The solution to the quadratic equation provides the time or times at which the projectile reaches a certain height, which is critical for determining other aspects of the projectile’s trajectory.

Acceleration Due to Gravity

The acceleration due to gravity is the constant rate at which objects accelerate towards the Earth, typically approximated as 9.8 m/s² near the surface. This constant value is used in the kinematic equations for analyzing the vertical component of motion, influencing how quickly an object speeds up while falling.

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